Problem: Solve for $x$ : $x^2 - x - 42 = 0$
Answer: The coefficient on the $x$ term is $-1$ and the constant term is $-42$ , so we need to find two numbers that add up to $-1$ and multiply to $-42$ The two numbers $-7$ and $6$ satisfy both conditions: $ {-7} + {6} = {-1} $ $ {-7} \times {6} = {-42} $ $(x {-7}) (x + {6}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -7) (x + 6) = 0$ $x - 7 = 0$ or $x + 6 = 0$ Thus, $x = 7$ and $x = -6$ are the solutions.